# How do you remove discontinuity of #f(x) = (x^4 - 1)/(x-1)#?

By signing up, you agree to our Terms of Service and Privacy Policy

To remove the discontinuity of the function f(x) = (x^4 - 1)/(x-1), we can use algebraic manipulation. The function has a discontinuity at x = 1 because the denominator becomes zero at that point. To remove this discontinuity, we can factorize the numerator as a difference of squares: x^4 - 1 = (x^2 + 1)(x^2 - 1). Then, we can simplify the function as f(x) = (x^2 + 1)(x^2 - 1)/(x-1). Now, we can cancel out the common factor of (x-1) in the numerator and denominator, resulting in f(x) = (x^2 + 1)(x + 1). This new function, f(x) = (x^2 + 1)(x + 1), does not have a discontinuity at x = 1.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the limit #(x+5)(1/(2x)+1/(x+2))# as #x->0^+#?
- How do you determine the limit of #(x^2-2x)/(x^2-4x+4)# as x approaches 2-?
- How do you find the limit of #(x^2+x-6)/(x^2-9)# as #x->-3#?
- How do you find the limit of #(1/x-1/2)/(x-2)# as #x->2#?
- How do you find the limit #ln(x^2+1)/x# as #x->0#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7